Optimal. Leaf size=13 \[ -\frac{x^3}{3}-x+\tanh ^{-1}(x) \]
[Out]
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Rubi [A] time = 0.0229495, antiderivative size = 13, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.231 \[ -\frac{x^3}{3}-x+\tanh ^{-1}(x) \]
Antiderivative was successfully verified.
[In] Int[x^5/(x - x^3),x]
[Out]
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Rubi in Sympy [A] time = 4.68189, size = 8, normalized size = 0.62 \[ - \frac{x^{3}}{3} - x + \operatorname{atanh}{\left (x \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**5/(-x**3+x),x)
[Out]
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Mathematica [B] time = 0.00682492, size = 29, normalized size = 2.23 \[ -\frac{x^3}{3}-x-\frac{1}{2} \log (1-x)+\frac{1}{2} \log (x+1) \]
Antiderivative was successfully verified.
[In] Integrate[x^5/(x - x^3),x]
[Out]
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Maple [A] time = 0.002, size = 22, normalized size = 1.7 \[ -{\frac{{x}^{3}}{3}}-x-{\frac{\ln \left ( -1+x \right ) }{2}}+{\frac{\ln \left ( 1+x \right ) }{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^5/(-x^3+x),x)
[Out]
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Maxima [A] time = 1.3692, size = 28, normalized size = 2.15 \[ -\frac{1}{3} \, x^{3} - x + \frac{1}{2} \, \log \left (x + 1\right ) - \frac{1}{2} \, \log \left (x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-x^5/(x^3 - x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.204217, size = 28, normalized size = 2.15 \[ -\frac{1}{3} \, x^{3} - x + \frac{1}{2} \, \log \left (x + 1\right ) - \frac{1}{2} \, \log \left (x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-x^5/(x^3 - x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.170204, size = 19, normalized size = 1.46 \[ - \frac{x^{3}}{3} - x - \frac{\log{\left (x - 1 \right )}}{2} + \frac{\log{\left (x + 1 \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**5/(-x**3+x),x)
[Out]
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GIAC/XCAS [A] time = 0.219067, size = 31, normalized size = 2.38 \[ -\frac{1}{3} \, x^{3} - x + \frac{1}{2} \,{\rm ln}\left ({\left | x + 1 \right |}\right ) - \frac{1}{2} \,{\rm ln}\left ({\left | x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-x^5/(x^3 - x),x, algorithm="giac")
[Out]